Observations on burst strength (Ib/in2) were obtained both for test nozzle closure welds and for production canister nozzle welds. Test 7200 6100 7300 7300 8000 7400 7300 7300 8000 6700 8300 Cannister 5250 5625 5900 5900 5700 6050 5800 6000 5875 6100 5850 6600 A comparative boxplot is given below. Test Nozle - Cannister-
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- Observations on burst strength (lb/in2) were obtainedboth for test nozzle closure welds and for productioncannister nozzle welds (“Proper Procedures Are theKey to Welding Radioactive Waste Cannisters,”Welding J., Aug. 1997: 61–67).Test 7200 6100 7300 7300 8000 74007300 7300 8000 6700 8300Cannister 5250 5625 5900 5900 5700 60505800 6000 5875 6100 5850 6600Construct a comparative boxplot and comment on interestingfeatures (the cited article did not include such a picture, but the authors commented that they had lookedat one).Suppose that samples of polythene bags from two manufacturers A and B are tested by a prospective buyer for bursting pressure, with the following results: If the prices are the same, which manufacture’s bags would be preferred by the buyer? Why?The joint PDF of the random variables X and Y is constant on the region (x,y):x≥0∩yleq1∩−0.5≤x−y≤0, shown in the image below, and is zero outside. Determine P(Y>0.5|X<0.5)
- An ecologist wishes to mark off a circular sampling region having radius 10 m. However,the radius of the resulting region is actually a random variable R with pdf f(x) = { 3/4[ 1- (10 - r)2 ] 9 ≤ r ≤ 11 0 otherwise What is the expected area of the resulting circular region?In a survey of 180 females who recently completed high school, 75% were enrolled in college. In a survey of 160 males who recently completed high school, 70% were enrolled in college. At α=0.07, can you reject the claim that there is no difference in the proportion of college enrollees between the two groups? Assume the random samples are independent. Complete parts (a) through (e). Find the critical value(s) and identify the rejection region(s).A researcher is using a two-tailed hypothesis test with α = 0.05 to evaluate the effect of a treatment. If the boundaries for the critical region are t = ± 2.080, then how many individuals are in the sample?
- What is the Marginal PDF of f(x)=2? Is the event independent?ONLY THE LAST ONE Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 5.9 7.2 7.3 6.3 8.1 6.8 7.0 7.5 6.8 6.5 7.0 6.3 7.9 9.0 8.4 8.7 7.8 9.7 7.4 7.7 9.7 8.2 7.7 11.6 11.3 11.8 10.7 The data below give accompanying strength observations for cylinders. 6.5 5.8 7.8 7.1 7.2 9.2 6.6 8.3 7.0 8.3 7.8 8.1 7.4 8.5 8.9 9.8 9.7 14.1 12.6 11.9 Prior to obtaining data, denote the beam strengths by X1, . . . , Xm and the cylinder strengths by Y1, . . . , Yn. Suppose that the Xi's constitute a random sample from a distribution with mean μ1 and standard deviation σ1 and that the Yi's form a random sample (independent of the Xi's) from another distribution with mean μ2 and standard deviation σ2. (a) Use rules of expected value to show that X − Y is an unbiased estimator of μ1 − μ2. E(X − Y) = E(X) − E(Y) = μ1 − μ2 E(X − Y) = E(X) − E(Y) 2 = μ1 − μ2 E(X − Y) = nm E(X) − E(Y) = μ1 − μ2 E(X −…We have a random variable X and Y that have the joint pdf f(x) = {1 0<x<1, 0<y<1} {0 otherwise} If U = Y-X2 , what would the pdf of the random variable U be? What is the support for the random variable U? Would there be any critical points? (use CDF technique)
- Two six-sided dice are rolled, and the random variable X is defined as the sum of the two numbers. Fill in the partial pdf for X.a. What is the probability that the lifetime X of the first component exceeds 3? b. What are the marginal pdf's of X and Y? Are the two lifetimes independent? x. What is the probability that the lifetime of at least one component exceeds 3?Suppose {Xi} are iid 〜Unif(0,θ). Consider the test Ho : θ=θo against H1 :θ<θo Use the likelihood ratio test to show that the critical region C has the form C={(x1,...xn)|yn≤cθo} Find c in term of the significant level a and θo. .